## Click to download the playlist as a pdf: Liberal Arts Mathematics

PROBLEM SOLVING

Introduction to Percent

Ex 1: Relating Fractions, Decimals, and Percents

Ex 2: Relating Fractions, Decimals, and Percents

The Percent Equation

Ex 1: Solve a Percent Problem Using a Percent Equation

Ex 2: Solve a Percent Problem Using a Percent Equation

Ex 3: Solve a Percent Problem Using a Percent Equation

Ex: Determine the Percent of a Number Using a Bar Graph

Ex: Change, Absolute Change, and Relative Change

Percent of Change

Ex 1: Determine a Percent of Change (decrease)

Ex 2: Determine a Percent of Change (increase)

Ex: Tax Percent Application - Find the Amount of FICA tax paid

Ex: Percent Applications - Changing Bases of Relative Change

Ex: Percent of Original Price Paid After Two Percentage Discounts

Ex: Weighted Average - Determine an Ending Percent or Grade of a Weighted Average

Ex: Proportion Application - Estimate Cost Based Upon Area

Ex: Proportion Application - Estimate Cost Based Upon Area

Rates and Unit Rates

American Unit Conversions

Perimeter and Area Formulas

Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour

Unit Conversion Application - Number of Lemons for a Lemon Pie

Ex: Determine the Width of a Canyon Based Upon an Echo Time

Ex: Volume Conversion to Determine the Number of Cubic Yards of Soil Needed

MEASUREMENT / GEOMETRY

Rates and Unit Rates

American Unit Conversions

Metric Unit Conversions

Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour

Unit Conversion Application - Number of Lemons for a Lemon Pie

Ex: Determine the Width of a Canyon Based Upon an Echo Time

Perimeter and Area Formulas

Ex: Volume of a Cylinder

Ex: Volume of a Sphere

Ex 2B: Find the Measure of an Interior Angle of a Triangle

VOTING THEORY

Introduction to Voting Theory and Preference Tables

Ex: Reading a Preference Table (Voting Theory)

Voting Theory: Fairness Criterion

Voting Theory: Plurality Method and Condorcet Criterion

Ex: Determine the Least Number of Votes Needed Using the Plurality Method

Voting Theory: Insincere Voting / Strategic Voting

Voting Theory: Instant Runoff Voting

Voting Theory: Monotonicity Criterion Using Instant Runoff Voting

Voting Theory: Borda count

Voting Theory: Copeland's Method

Voting Theory: Approval Voting

WEIGHTED VOTING

Introduction to Weighted Voting

Weighted Voting: Coalitions and Critical Players

Weighted Voting: The Banzhaf Power Index

Weighted Voting: The Shapley-Shubik Power Index

FAIR DIVISION

Introduction to Fair Division

Fair Division: The Divider-Chooser Method

The Divider-Chooser Method of Fair Division – Why It Is Meant Only for 2 Players

Fair Division: The Lone Divider Method

The Lone Divider Method: Why It Doesn't Pay To Be Greedy

Fair Division: The Last Diminisher Method

Fair Division: The Moving Knife Method

Fair Division: The Sealed Bid Method

APPORTIONMENT

Introduction to Apportionment

Apportionment: Hamilton's Method

Apportionment: The Alabama Paradox

Apportionment: The New States Paradox

Apportionment: The Population Paradox

Apportionment: Jefferson's Method

Apportionment: Webster's Method

Apportionment: Huntington-Hill Method

Apportionment: Lowndes' Method

GRAPH THEORY

Introduction to Graph Theory

Graph Theory: Dijkstra's Algorithm

Graph Theory: Euler Paths and Euler Circuits

Graph Theory: Fleury's Algorthim

Graph Theory: Eulerization

Graph Theory: Hamiltonian Circuits and Paths

Graph Theory: The Brute Force Algorithm

Graph Theory: Number of Routes and Circuits of a Complete Graph

Graph Theory: Nearest Neighbor Algorithm (NNA)

Graph Theory: Repeated Nearest Neighbor Algorithm (RNNA)

Graph Theory: Sorted Edges Algorithm (Cheapest Link Algorithm)

Graph Theory: Spanning Trees

Graph Theory: Kruskal's Algorithm

SCHEDULING

Introduction to Scheduling

Scheduling: The List Processing Algorithm Part 1

Ex: Scheduling - Create a Priority List Using the Decreasing Time Algorithm

Ex: Scheduling - Create a Priority List Using the Critical Path Algorithm

Scheduling: The List Processing Algorithm Part 2

Ex: Create a Schedule with Three Processors Using the List Processing Algorithm

Scheduling: The Decreasing Time Algorithm

Ex: Create a Priority List and Schedule Using the Decreasing Time Algorithm and List Processing Algorithm

Scheduling: The Critical Path Algorithm Version 1 (Part 1)

Scheduling: The Critical Path Algorithm Version1 (Part 2)

Scheduling: The Back Flow Algorithm Part 1

Scheduling: The Back Flow Algorithm Part 2

GROWTH

Linear Growth: Recursive and Explicit Equations Part 1

Linear Growth: Recursive and Explicit Equations Part 2

Ex: Find an Explicit Equation for Linear Growth and Determine and Input for An Output

Ex: Write an Explicit Equation to Model Linear Growth

Ex: Write a Recursive and Explicit Equation to Model Linear Growth

Exponential Growth: Recursive and Explicit Equations Part 1

Exponential Growth: Recursive and Explicit Equations Part 2

Ex: Find an Recursive and Explicit Equation for Exponential Growth Given r

Compare Linear and Exponential Growth Using Recursive and Explicit Equations

Solving Exponential Equations for Time using Common Logs

Logistic Growth: Recursive Equations

Logistic Growth: Overshoot and Collapse

FINANCE

The Simple Interest Formula

Ex: Determine an Account Balance Using Simple Interest

Compounded Interest

Ex 1: Compounded Interest Formula – Quarterly

Ex: Compounded Interest Formula - Determine Deposit Needed (Present Value)

Solving Exponential Equations for Time using Common Logs

Ex 2: Compounded Interest with Logarithms

Derive the Value of an Annuity Formula

Determining the Value of an Annuity

Determine the Value of an Annuity with a TI84

Payout Annuity Formula - Part 1

Payout Annuity Formula - Part 2

The Installment Loan Formula

The Installment Loan Formula: Determining Remaining Balance

Annuity Formula and Loan Formula: Solving for Time

Ex: TI84 TVM Solver - Find the Present Value of a Loan Given Monthly Payment

Ex: TI84 TVM Solver - Present Value with Compounded Interest

TI84 TVM Solver - Find Present Value of an Payout Annuity

Ex: TI84 TVM Solver - Find Payout Annuity Monthly Payment Given Present Value

Ex: TI84 TVM Solver - Find a Monthly Loan Payment

Ex: TI84 TVM Solver - Future Value with Compounded Interest

Ex: TI84 TVM Solver - Find Annuity Monthly Payment Needed for Given Future Value

Ex 1: TI84 TVM Solver - Future Value of an Annuity

Ex 2: TI84 TVM Solver - Future Value of an Annuity

STATISTICS

Introduction to Statistics

Statistics: Sampling Methods

Statistics Control Groups and the Placebo Effect

Statistics: Introduction to Experiments and Confounding

Statistics: Sources of Bias

DESCRIBING DATA

Describing Categorical Data Using a Bar Graph, Pareto Chart, Pie Chart, and Pictogram

Describing Quantitative Data Using a Histogram

Describing Quantitative Data Using Mean, Median, and Mode

Ex: Find the Mean and Median of a Data Set Given in a Frequency Table (odd)

Ex: Find the Mean and Median of a Data Set Given in a Frequency Table (even)

Describing Quantitative Data: Range and Standard Deviation

Describing Quantitative Data: Quartiles and the Five Number Summary

Ex: Mode, Mid-range, Range, Standard Deviation Using Range Rule of Thumb

Ex: Complete a Frequency Table

Ex: Find the Sample Size and Percent of Sample From a Bar Graph

Ex: Make a Prediction using the Sample Statistic (Marbles)

Ex: Determine a Sample Statistics and Make a Prediction using the Statistic

Ex: Find the Percent of an Amount Using a Percent in Pie Chart

Ex: Find the a Percent of a Total Using an Amount in Pie Chart

Describing Quantitative Data using a Box Plot

Ex 1: Compare Two Box Plot Values

Ex 2: Compare Two Box Plot Values

Ex: Determine the Percent Below a Quartile Using a Box Plot

Ex: Determine a Five Number Summary (Odd)

Ex: Determine a Five Number Summary (Even)

Ex: Determine the Five Number Summary from a Box Plot

Ex: Interpret the Mean and Standard Deviation of Two Data Sets

Ex: Calculate the Sample Standard Deviation

TI84 One Variable Statistics Overview

TI84 One Variable Statistics Overview with Frequency Table

TI84 One Variable Statistics - Five Number Summary

TI84 One Variable Statistics - Mean

TI84 One Variable Statistics - Mean and Median

TI84 One Variable Statistics - Mean and Median Using a Frequency Table

TI84 One Variable Statistics - Standard Deviation

TI84 One Variable Statistics - Standard Deviation From a Frequency Table

Normal Distribution / Sampling Distribution and Estimations

Introduction to the Normal Distribution

Ex 1: Normal Distribution - Use the Empirical Rule

Ex 2: Normal Distribution - Use the Empirical Rule

Ex 1A (Norm Dist) Use the 68-95-99.7 Rule to Find the Percent of Data Between Given Data Values

Ex 1B (Norm Dist) Use the TI84 to Find the Percent of Data Between Given Data Values

Ex 2A (Norm Dist) Use the 68-95-99.7 Rule to Find the Percent of Data Between Given Data Values

Ex 2B (Norm Dist) Use the TI84 to Find the Percent of Data Between Given Data Values

Normal Distribution: Z-Scores

Normal Distribution: Find Probability Using With Z-scores Using the TI84

Normal Distribution: Find Probability Using With Z-scores Using Tables

Normal Distribution: Find Probability of Data Values Using the TI84

Normal Distribution: Find Probability of Data Values Using Tables

Ex 1: Find the Probability of a Z-score Being Less Than a Given Value on a Newer TI84

Ex 2: Find the Probability of a Z-score Being Greater Than a Given Value on a Newer TI84

Ex 3: Find the Probability of a Z-score Being Between Two Z-score on a Newer TI84

Ex 1: Find a Z-score Given the Probability of Z Being Less Than a Given Value

Ex 2: Find a Z-score Given the Probability of Z Being Greater Than a Given Value

Ex 1: Find a Probability Given a Data Value Involving a Normal Distribution - P(x<n) TI84

Ex 2: Find a Probability Given a Data Value Involving a Normal Distribution - P(x>n) TI84

Ex 3: Find a Probability Given a Data Value Involving a Normal Distribution - P(m<x<n) TI84

Ex 1: Find a Data Value Given a Probability Involving a Normal Distribution - TI84

Ex 2: Find a Data Value Given a Probability Involving a Normal Distribution - TI84

PROBABILITY

Introduction to Probability

Ex: Basic Example of Finding Probability - Running a Red Light

Ex: Basic Example of Finding Probability From a Table

Ex: Find Basic Probabilities When Rolling One Fair Die

Ex: Find Basic Probabilities Using a Deck of Cards

Ex: Basic Probability Review Using Marbles

Probability: The Probability of the Complement of an Event

Probability: The Probability of Independent Events

Probability: Determine the Probability of the Union of Events

Probability: Probability of Mutually Exclusive Events

Probability: Probability of Events Not Mutually Exclusive

Ex: Determine a Probability with AND using a Table

Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive - No Formula)

Ex: Determine the Probability of the Union of Two Events (OR)

Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive)

Ex: Find the Probability of a Complement Using a Table

Ex: Find the Probability of Dependent Events Two Ways

Ex 2: Find the Probability of Dependent Events

Probability: Conditional Probability

Ex: Find Conditional Probability Using a Table

Ex: Determine Conditional Probability from a Table

Probability: Bayes’ Theorem

The Counting Principle

Simplifying Factorial Expressions

Permutations

Combinations

Counting Problems

Probability: Determining Probability Using Combinations

Determining Probability

Expected Value

Ex: Expected Value

Ex: Determine Odds from Given Information (Basic)

Ex: Determine Probability Given Odds

HISTORICAL COUNTING SYSTEMS

Inca Counting Boards

The Inca Quipu

Convert Numbers in Different Bases to Base Ten

Ex: Convert Base-12 to Base-10

Convert Numbers in Base Ten to Different Bases: Remainder Method

Convert Numbers in Base Ten to Different Bases: Calculator Method

The Mayan Number System: Writing Mayan Number in Base 10

The Mayan Number System: Writing Base 10 Numbers as Mayan Number (base 20)

The Mayan Number System: Addition of Mayan Numbers

CRYPTOGRAPHY

Cryptograph: Substitution Cipher (Caeser Cipher)

Cryptography: Transposition Cipher

Cryptography: Caesar Cipher With Shift

Modular Arithmetic

SETS

Introduction to Set Theory

Introduction to Subsets

Set Operations and Venn Diagrams - Part 1 of 2

Set Operations and Venn Diagrams - Part 2 of 2

Solving Problems Using Venn Diagrams

Ex: Find the Union and Intersection of Two Sets Using a Venn Diagram

Ex: Find the Union and Intersection of Two Sets Without a Venn Diagram

Ex: Find the Intersection of a Set and A Complement Using a Venn Diagram

Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (short)

Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (short)

Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (long)

Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (long)

Ex: Determine Cardinality of the Intersection of Two Sets Using a Venn Diagram

Ex: Determine Cardinality of the Intersection of Two Sets Without Using Venn Diagram

Ex: Determine Cardinality of Various Sets Given a Venn Diagram of Three Sets

Ex: Determine Cardinality of the Intersection of Three Sets Using a Venn Diagram

Ex: Determine Cardinality of the Intersection of Three Sets Without Using Venn Diagram

Ex: Find the Number of Element in the Intersection of Two Sets Using a Venn Diagram

Ex: Set Problem Solving - Find the Number of Element in the Intersection of Two Sets Using a Formula

Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Venn Diagram

Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula

Ex 2: Find the Number of Element in the Union of Two Sets Using a Venn Diagram

Ex 2: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula

Ex: Determine How Many Elements in a Set With a Venn Diagram (Movies)

Ex: Determine How Many Elements in a Set Without a Venn Diagram (Movies)

Ex 1: Problem Solving With Venn Diagrams (Cardinality of Intersection)

Ex 2: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)

Ex 3: Problem Solving With Venn Diagrams (Cardinality of Complement of (A Union B)

Ex 4: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)

Logic

If-Then Statements and Converses

The Converse, Contrapositive, and Inverse of an If-Then Statement

Truth Tables for Compound Statements

Truth Tables for Conditional Statements

Truth Table for the Biconditional Statement

Truth Tables: Showing Statements are Equiv